For the Burg entropy, the entropic involution is always possible
[1]} because it tends to \(-\infty \)  at the border of
positivity. The same is true, for the relative entropy of the form
\(S=-\beta ^{-1}\sum W_i ((W_i/f_i)^{\beta }-1)\)  that tends to the Burg
entropy when \(\beta \rightarrow 0\)  [2]}. This negative
brunch of the relative Tsallis entropy is less known. The
standard Tsallis entropy [3]} is finite at the border of
positivity, hence, collisions with entropy preservation are not
always possible for it.
